Rossouw, who scored 125 in last year’s final, also abetted James Vince’s 79 in a century fourth-wicket stand.
Gareth Berg laid the foundations of the victory with his maiden one-day five-wicket haul and was brilliantly assisted by Mason Crane’s 3-42.
Berg rolled back the years to grab 5-26, while leg-spinner Crane appeared back to his best as Lancashire were restricted to 241.
Meanwhile, Lancashire were condemned to their ninth straight List A semi-final defeat, as Hampshire aim to be the first side since Sussex in 2008 and 2009 to win consecutive one-day competitions.
Saqib Mahmood struck with the fifth ball of Hampshire’s reply when he tucked Tom Alsop up to find an inside edge behind.
The fast bowler followed it up with two more scalps; Aneurin Donald slashed to point and then Sam Northeast chopped onto his own stumps.
That left Hampshire 23-3 and Mahmood celebrating figures of 3-20 from his first six-over spell.
Vince ignored the wobble happening at the other end as he dug Hampshire out of the mire with a 55-ball half century.
The captain, who was released by the ECB to play, guided Rossouw through a sticky start into a 122-run partnership for the fourth wicket.
South African Rossouw made it to 50, off 69 balls, with back-to-back boundaries off James Anderson.
The stand was ended by a sharp piece of fielding from Steven Croft at cover and a foolish piece of running.
But Rossouw continued to slide through the gears, while Liam Dawson found important boundaries at the other end in a 59-run collaboration.
Dawson was dropped on 26 but did not capitalise as he skied soon after and Rossouw was bowled off his pads.
However, Hampshire made it back to Lord’s when James Fuller scored the winning runs with six balls left.
Lancashire had won the toss and elected to bat first.
Keaton Jennings and Liam Livingstone put on 37 for the first wicket before the latter was bounced out by Fidel Edwards, Crane taking a simple catch on the boundary.
Alsop once again proved his increasing stock behind the wicket when he produced a stunning full-length dive to catch Croft.
Jennings and Jake Lehmann rebuilt again with a 67-run stand, which saw the England opener move to his fifth One Day Cup 2018 half-century in 56 balls.
Crane entered the attack to have Jennings castled with a straight ball and Dane Villas caught slapping to Vince at extra cover.
Australian Lehmann notched his 50 in 53 deliveries but was another victim of failing to convert when he slog swept Dawson to Fuller on the deep midwicket boundary.
From that point Hampshire took control, stifling Rob Jones to 38 before Crane picked up the last of his scalps when slogged to long-on.
Berg cleared up the tail, seeing off Josh Bohannon and Graham Onions before bowling Anderson and having Mahmood caught by Vince to bowl Lancashire out.